A fully abstract model for a nonuniform concurrent language with parameterization and locality

Abstract

Full abstraction of a denotational model w.r.t. operational ones for a concurrent language L is investigated. The language is nonuniform in that the meaning of atomic statements generally depends on the current state; it has parameterization with channel- and value-parameters and locality in the form of local variables and local channels, in addition to more conventional constructs: value assignments to variables, parallel composition with CSP/CCS-like communication, nondeterministic choice, and recursion. First two operational models OL and O L * for L are introduced in terms of a Plotkin-style transition system. Both models are linear in that they map each statement to the set of its possible execution paths of a certain kind; the second model O L * is more abstract than the first one in that O L * ignores states while OL involves them. Then a denotational model D is defined compositionally using interpreted operations of the language, with meanings of recursive programs as fixed points in an appropriate complete metric space. The the full abstraction of D w.r.t. OL and O L * established. That is, it is shown for O=OL, O L * that D is most abstract of those models C which are compositional and more distinctive than O.